Problem: Suppose the point $(1,2)$ is on the graph of $y=\frac{f(x)}2$. Then there is one point which must be on the graph of $y=\frac{f^{-1}(x)}{2}$. What is the sum of that point's coordinates?
Answer: Since $(1,2)$ is on the graph of $y=\frac{f(x)}2$, we know that $$2 = \frac{f(1)}{2},$$which implies that $f(1)=4$. Therefore, $f^{-1}(4)=1$, which implies that $\left(4,\frac12\right)$ is on the graph of $y=\frac{f^{-1}(x)}{2}$. The sum of this point's coordinates is $\boxed{\frac 92}$.